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Zumdahl’s Chapter 11. Solutions. Solution Composition Concentrations H solution Hess’s Law undersea Solubilities Henry’s Law: Gases and Raoult’s Law Temperature Effects. Colligative Properties T BP Elevation T FP Depression Osmotic Pressure van’t Hoff Factor

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chapter contents
Solution Composition

Concentrations

Hsolution

Hess’s Law undersea

Solubilities

Henry’s Law: Gases

and Raoult’s Law

Temperature Effects

Colligative Properties

TBP Elevation

TFP Depression

Osmotic Pressure

van’t Hoff Factor

Colloids and Emulsions

Chapter Contents
solution composition
Solution Composition
  • Molarity, M = moles solute / liter sol’n.
    • Cannot be accurately predicted for mixtures because partial molar volumes vary.
    • If volumes don’t add, masses and moles do!
  • Molality, m = moles solute / kg solvent
    • Not useful in titration unless density known.
    • Useful in colligative effects.
  • Mole fraction, XA = moles A / total moles
conc of 50 by wt naoh
Conc. of 50% by wt. NaOH
  • Density at 20°C is 1.5253 g cm3
    •  each liter of solution weighs 1525.3 g
    • ½ that mass is NaOH, or 762.65 g
    • nNaOH = 762.65 g [ 1 mol/39.998 g ] = 19.067
    • [NaOH] = 19.067M but also
    • 19.067 mol / 0.76265 kg H2O = 25.001mand
    • nwater = 762.65 g [ 1 mol/18.016 g ] = 42.332
    • XNaOH =19.067 /(19.067+42.332)=0.31054
100 cc ea h 2 o c 2 h 5 oh
100 cc ea. H2O & C2H5OH
  • Want Proof? 50% by Volume 100 proof
  • Want Volume? Need densities!
    • At 20°C,  = 0.99823 & 0.79074 g/cc, resp.
    •  sol’n. mass = 99.823+79.074 = 178.897 g
    • By mass: 100%(79.074 / 178.897) = 44.201%
    • From tables:  = 0.92650 g/cc
    • V = 178.897 g/0.92650 g/cc = 193.09 cc
      •  It’s really 2 100cc / 193.09 cc = 103.58 proof
conceptual mixing enthalpies

Expand both solvent and solute

  • at the expense of H1 and H2
  • in lost intermolecular
  • interactions.
Conceptual Mixing Enthalpies
  • Merge the
  • expanded liquids
  • together recovering
  • H3 from the
  • new interactions.

But even if it

requires heat,

mixing may

well happen

since entropy

favors it!

3. If the exothermic

mixing exceeds

the endothermic

expansion, there

will be a net exo-

thermic heat of

solution.

underwater hess s law
Underwater Hess’s Law
      • Unrelated to basket weaving.
  • Since solutions are fluid, they need not expand then mix, requiring “upfront” $$.
  • Instead they acquire AB interaction as they lose AA and BB ones; pay as you go.
  • Hess doesn’t care; the overall enthalpy change$ will be the same.
solubilities
Solubilities
  • It’s true that which of A or B is the solute or solvent is mere naming convention …
      • Which was the solute in that 50% cocktail?
  • Still solutes with low solubility are surely in the mole fraction minority.
  • And it is worthwhile asking what state parameters influence their solubility?
gas solubilities
Gas Solubilities
  • No doubt about it: pressure influences solubility. And directly.
      • CO2 in soft drinks splatter you with dissolution as you release the pressure above the liquid.
  • Henry’s Law codifies the relationship:
  • PA = kH•[A(aq)] (kH is Henry’s constant)
    • It applies only at low concentrations; so
    • It applies not at all to strongly soluble gases!
raoult s and henry s laws
Apply at opposite extremes.

Raoult when X~1

Henry when X~0

So Raoult to solvent and Henry to solute.

When XB is small, XB=[B]/55.51M for [water]=55.51M

Henry’s OK with X.

P°B

P°A

P

k’H;B

k’H;A

XA

0

1

P = P° X

P kH’ X

Raoult’s and Henry’s Laws
raoult vs henry difference
Raoult vs. Henry Difference
  • When X~1, the solvent is not perturbed by miniscule quantities of solute. Solvent vaporization is proportional to solvent molecules at solution’s surface. Raoult
  • When X~0, solute is in an utterly foreign environment, surrounded only by solvent. kH reflects the absence of A-A interaction, and Henry applies.
solubility and temperature
Solubility and Temperature
  • Sometimes the AB interactions are so much weaker than AA or BB that A and B won’t mix even though entropy favors it.
    • Since T emphasizes entropy, some of the immiscible solutions mix at higher T.
  • Solidsolubilities normally rise with T.
    • Exceptions are known … like alkali sulfates.
gases flee hot solutions
Gases Flee Hot Solutions
  • You boiled lab water to drive out its dissolved gases, especially CO2.
    • That’s why boiled water tastes “flat.”
      • Genghis Khan invented tea (cha) to flavor the water his warriors refused to boil for their health as they conquered Asia and Eastern Europe.
  • Increased T expands Vgas, making it more favored by entropy vs. dissolved gas.
    • This time, no exceptions!
changed phase changes
The Phase Diagram

Mixing in a solute lowers solvent Pvapor

So TBP must rise.

Since the solvent’s solid suffers no Pvapor change, TFP must fall.

Liquid span must increase in solution.

P

T

Changed Phase Changes
elevating depressions
Elevating Depressions
  • Both colligative properties arise from the same source: Raoult’s Law.
  • Thermo. derivations of resulting T give:
    • Freezing Point Depression:
      • TFP = –Kf msolute where Kf~RTFP2 / Hfusion
    • Boiling Point Elevation:
      • TBP = +Kb msolute where Kb~RTBP2 / Hvap
  • Kf > Kb since Hfusion < Hvap
practical phase changes
Antifreeze / Summer Coolant are the same

Ethylene glycol (1,2-Ethanediol) is soluble in the radiator water, non-corrosive, nonscaling, and raises the boiling point in summer heat while lower-ing freezing point in winter.

“Road salt” is CaCl2 now since NaCl corrodes cars.

Practical Phase Changes
col liga tive utility
Colligative Utility
  • Ligare means “to bind.” These features are bound up with just numbers of moles.
      • NOT the identity of the molecules!
  • Indeed, Kf and Kb are seen not to depend on solute properties but on solvent ones.
    • So they’re used to count solute moles to convert weights to molar weights!
      • Not sensitive enough for proteins, MW~10 kg
exquisite sensitivity
Exquisite Sensitivity
  • To count protein moles, we need Osmotic Pressure that is very sensitive to [solute].
    • Solvent will diffuse across a membrane to dilute a concentrated solute solution.
    • If the solute is too large (protein!) to diffuse back, the volumemust increase.
    • Rising solution creates (osmotic) pressure to an equilibrium against further diffusion.
mw by osmotic pressure

MW by Osmotic Pressure, 
  • Thermodynamic derivation of the balance between  & diffusion on the equilibrium gives: V = nRT(!) or = MRT
    • E.g., 0.5 g in 50 cc yields 10 cm of pressure at 25°C (so RT = 24.5 atm L /mol)
    • 10 cm (1 ft/30.5 cm) (1 atm/33 ft) = .010 atm
    • [protein] =  / RT = 0.00041 mol/L
    • Wt = 0.5 g/0.05 L = 10 g/L MW = 24 kg
moles of what
Moles of What?
  • Doesn’t matter if property’s colligative.
  • Counts moles of ions if solute dissociates.
  • van’t Hoff Factor, i, measures ionization.
    • i multiplies molality in any of the colligative expressions to show apparent moles present.
      • It’s a stand-in for non-idealities too; pity.
    • So in 0.001mK3PO4, i should be nearly 4, and colligative properties see 0.004m?NO!
weak electrolyte corrections
Weak Electrolyte Corrections
  • PO43– is a conjugate base of HPO42–
    • Ka3 = 4.810–13so Kb1 = Kw/Ka3 = 0.021 for PO43– + H2O  HPO42– + OH–
    • Equilibrium lies to left, so start with [OH–] = [HPO42–] = 0.001–xand [PO43–] = x
    • (0.001–x)2 / x = 0.021 or x ~ 4.810–5 ~ 0
    • Counting K+, total moles ~ 0.003+2(0.001)
    • Soi ~ 0.005/0.001 = 5not 4. (4.95 with care)
reverse osmosis
Reverse Osmosis
    • If dilution across a semipermeable (keeps out solute) membrane builds pressure,
  • Pressure should be able to squeeze water back out of a solution! …if the membrane survives.
  • Desalination plants are critical in desert nations like the Gulf States & N. Africa.
      • Waste water is much more (salt) concentrated, an environmental hazard to local sea life unless ocean currents are swift enough to dilute it.
when is a solution not a solution
When is a SolutionNot a Solution?
      • When it’s a problem? 
  • Insoluble materials precipitate out of a solution at a rate that increases with their mass. So smallparticlesstay suspended.
  • With particle sizes of 1 m to 1 nm such suspensions are called colloids.
    • Since visible ~ 0.5m, the larger colloids scatter visible light efficiently! (Tyndall effect)
taxonomy of suspensions
Taxonomy of Suspensions

Dispersed Material Phase

Dispersing Medium Phase

aqueous colloids

+

+

+

+

+

+

+

+

+

Aqueous Colloids
  • Particles might be charged and stabilized (kept from coagulating) by electrostatics.
    • Even neutral ones will favor adjacency of one charge which develops double layer (an oppositely charged ionic shell) to stabilize the colloid.
    • “Salting out” destroys the colloid by over-whelming the repulsions with ionic strength.
      • Small, highly charged ions work best, of course.
surface chemistry liquids
Surface Chemistry (liquids)
  • Colloid study, a subset of surface science.
  • Colloid molecules must be insoluble in the dispersing medium.
    • Solubility governed by “like dissolves like.”
    • But surface tensions play a role as well since solutes display surface excess concentration.
      • Interfaces between phases are not simply at the bulk concentrations; influences segregation.
surface chemistry solids
Surface Chemistry (solids)
  • Industrial catalysts for many processes are solids.
    • Atoms and molecules adhere, dissociate, migrate, reassociate, and desorb.
    • Efficiency scales with catalyst surface area.
    • Area measured by adsorbing monolayers of gas (N2 ) and observing discontinuities as monolayer is covered.